Two professors are applying for grants. Professor Jane has a probability of 0.68

Question

Two professors are applying for grants. Professor Jane has a probability of 0.68 of being funded. Professor Joe has probability 0.25 of being funded. Since the grants are submitted to two different federal agencies, assume the outcomes for each grant are independent. Give your answer to four decimal places. a. What is the probability that both professors get their grants funded b. What is the probability that at least one of the professors will be funded? c. What is the probability that Professor Jane is funded but Professor Joe is not? d. Given at least one of the professors is funded, what is the probability that Professor Ja ne is funded but Professor Joe is not?

Explanation / Answer

A) P(both get their grants funded) = 0.68 * 0.25 = 0.17

B) P(at least one of the professor will be funded) = 0.68 * 0.75 + 0.25 * 0.32+ 0.68 * 0.25 = 0.76

C) P(professor jane is funded but professor joe is not) = 0.68 * 0.75 = 0.51

D) P(professor jane is funded but professor joe is not funded | at least one of the professor is funded)

= 0.68 * 0.75/0.76

= 0.6711

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